Guedda, Mohammed; Kersner, Robert Self-similar solutions to the generalized deterministic KPZ equation. (English) Zbl 1024.35039 NoDEA, Nonlinear Differ. Equ. Appl. 10, No. 1, 1-13 (2003). Summary: Geometric properties of shape functions of self-similar solution to the equation \(u_t = u_{xx} + \lambda|u_x|^q\) are studied, \(\lambda\) and \(q\) are positive numbers. These shapes-the solutions of the corresponding nonlinear ODE-are of very different nature. The properties usually depend on three critical values of \(q\) (1, 3/2 and 2). For the range \(1<q<2\) the dependence of \(\lambda\) is more remarkable, for example there is no global existence in general. Cited in 11 Documents MSC: 35K55 Nonlinear parabolic equations 34A05 Explicit solutions, first integrals of ordinary differential equations 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations 35K65 Degenerate parabolic equations Keywords:surface growth; one space dimension; global existence; shape functions PDFBibTeX XMLCite \textit{M. Guedda} and \textit{R. Kersner}, NoDEA, Nonlinear Differ. Equ. Appl. 10, No. 1, 1--13 (2003; Zbl 1024.35039) Full Text: DOI